Abstract: In the problem of multi-target tracking, GM-CPHD filter can estimate recursively the targets’ information of the cardinality distribution and the intensity distribution simultaneously, and then the filtering results are more accuracy. However, one of its disadvantages is that the time complexity is high, especially in the case of a high noise rate, the filtering time is too long. The main reason is that the high computational complexity of the Elementary Symmetric Functions（ESF） in the update step of the algorithm. To solve this problem, this paper replaces the definition method with a recursive method to calculate ESF, and the efficiency of the GM-CPHD is improved. The experimental results show that the ESF calculated by the recursive method does not affect the accuracy of the filter, and can reduce its complexity.

Key words: target tracking, GM-CPHD filter, elementary symmetric function, time complexity, execution efficiency

摘要： 多目标跟踪问题中，GM-CPHD滤波算法能够同时递推估计势分布及强度分布信息，滤波精度较高。然而其缺点是时间复杂度较大，尤其是当杂波率较高时，滤波时间过长。导致该问题的主要原因是该算法更新步骤中的初等对称函数的计算复杂度很高。针对该问题，采用递推方法替换定义方法计算初等对称函数，提高了求解效率，降低了整个算法的时间复杂度。仿真结果表明，通过递推方法计算初等对称函数能够大大降低滤波时间复杂度，且不影响滤波精度。

关键词: 目标跟踪, GM-CPHD滤波, 初等对称函数, 时间复杂度, 执行效率